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SageMath
E = EllipticCurve("p1")
E.isogeny_class()
Elliptic curves in class 14157p
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 14157.m1 | 14157p1 | \([0, 0, 1, -79860, -8780940]\) | \(-360448000/4563\) | \(-713049169448187\) | \([]\) | \(42240\) | \(1.6598\) | \(\Gamma_0(N)\)-optimal |
| 14157.m2 | 14157p2 | \([0, 0, 1, 279510, -44753877]\) | \(15454208000/14480427\) | \(-2262821925401074323\) | \([3]\) | \(126720\) | \(2.2091\) |
Rank
sage: E.rank()
The elliptic curves in class 14157p have rank \(0\).
Complex multiplication
The elliptic curves in class 14157p do not have complex multiplication.Modular form 14157.2.a.p
sage: E.q_eigenform(10)
Isogeny matrix
sage: E.isogeny_class().matrix()
The \(i,j\) entry is the smallest degree of a cyclic isogeny between the \(i\)-th and \(j\)-th curve in the isogeny class, in the Cremona numbering.
\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
